Average Error: 13.8 → 10.6
Time: 13.6s
Precision: binary64
\[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
↓
\[\frac{{\left({\left(e^{\sqrt[3]{\log \left(1 \cdot \left(1 - \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(1 \cdot \left(1 - \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)\right)}\right)}\right)}^{\left(\sqrt[3]{\log \left(1 \cdot 1 - \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right) \cdot \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right)\right)}\right)}}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]
1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}
↓
\frac{{\left({\left(e^{\sqrt[3]{\log \left(1 \cdot \left(1 - \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(1 \cdot \left(1 - \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)\right)}\right)}\right)}^{\left(\sqrt[3]{\log \left(1 \cdot 1 - \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right) \cdot \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right)\right)}\right)}}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}
double code(double x) {
	return ((double) (1.0 - ((double) (((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (0.254829592 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-0.284496736 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (1.421413741 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-1.453152027 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * 1.061405429)))))))))))))))))) * ((double) exp(((double) -(((double) (((double) fabs(x)) * ((double) fabs(x))))))))))));
}
↓
double code(double x) {
	return (((double) pow(((double) pow(((double) exp(((double) cbrt(((double) log(((double) (1.0 * ((double) (1.0 - ((double) ((1.0 / ((double) pow(((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))), 2.0))) * ((double) (((double) cbrt(((double) pow(((double) (0.254829592 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-0.284496736 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (1.421413741 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-1.453152027 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * 1.061405429)))))))))))))))), 6.0)))) * ((double) pow(((double) exp(-2.0)), ((double) pow(((double) fabs(x)), 2.0)))))))))))))))))), ((double) cbrt(((double) log(((double) (1.0 * ((double) (1.0 - ((double) ((1.0 / ((double) pow(((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))), 2.0))) * ((double) (((double) cbrt(((double) pow(((double) (0.254829592 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-0.284496736 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (1.421413741 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-1.453152027 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * 1.061405429)))))))))))))))), 6.0)))) * ((double) pow(((double) exp(-2.0)), ((double) pow(((double) fabs(x)), 2.0)))))))))))))))))), ((double) cbrt(((double) log(((double) (((double) (1.0 * 1.0)) - ((double) (((double) (((double) cbrt(((double) pow(((double) (0.254829592 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-0.284496736 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (1.421413741 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-1.453152027 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * 1.061405429)))))))))))))))), 6.0)))) * ((double) pow(((double) exp(-2.0)), ((double) pow(((double) fabs(x)), 2.0)))))) * ((double) (1.0 * (1.0 / ((double) pow(((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x)))))), 2.0))))))))))))))) / ((double) (1.0 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * (((double) (0.254829592 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-0.284496736 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (1.421413741 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * ((double) (-1.453152027 + ((double) ((1.0 / ((double) (1.0 + ((double) (0.3275911 * ((double) fabs(x))))))) * 1.061405429)))))))))))))))) / ((double) exp(((double) pow(((double) fabs(x)), 2.0))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 13.8 bits

    \[1 - \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\]
  2. Using strategy rm

  3. Applied flip--Error: 13.8 bits

    \[\leadsto \color{blue}{\frac{1 \cdot 1 - \left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}\right)}{1 + \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}}\]

  4. SimplifiedError: 13.8 bits

    \[\leadsto \frac{\color{blue}{1 \cdot 1 - \frac{1}{\frac{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}{1}} \cdot \left(\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot {\left(e^{\left|x\right|}\right)}^{\left(2 \cdot \left(-\left|x\right|\right)\right)}\right)}}{1 + \left(\frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot e^{-\left|x\right| \cdot \left|x\right|}}\]

  5. SimplifiedError: 13.8 bits

    \[\leadsto \frac{1 \cdot 1 - \frac{1}{\frac{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}{1}} \cdot \left(\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot {\left(e^{\left|x\right|}\right)}^{\left(2 \cdot \left(-\left|x\right|\right)\right)}\right)}{\color{blue}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}}\]
  6. Using strategy rm

  7. Applied add-cbrt-cubeError: 10.6 bits

    \[\leadsto \frac{1 \cdot 1 - \frac{1}{\frac{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}{1}} \cdot \left(\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \color{blue}{\sqrt[3]{\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}}\right) \cdot {\left(e^{\left|x\right|}\right)}^{\left(2 \cdot \left(-\left|x\right|\right)\right)}\right)}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]

  8. Applied add-cbrt-cubeError: 13.8 bits

    \[\leadsto \frac{1 \cdot 1 - \frac{1}{\frac{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}{1}} \cdot \left(\left(\color{blue}{\sqrt[3]{\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}} \cdot \sqrt[3]{\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}\right) \cdot {\left(e^{\left|x\right|}\right)}^{\left(2 \cdot \left(-\left|x\right|\right)\right)}\right)}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]

  9. Applied cbrt-unprodError: 10.6 bits

    \[\leadsto \frac{1 \cdot 1 - \frac{1}{\frac{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}{1}} \cdot \left(\color{blue}{\sqrt[3]{\left(\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(\left(\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right) \cdot \left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)\right)}} \cdot {\left(e^{\left|x\right|}\right)}^{\left(2 \cdot \left(-\left|x\right|\right)\right)}\right)}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]

  10. SimplifiedError: 10.6 bits

    \[\leadsto \frac{1 \cdot 1 - \frac{1}{\frac{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}{1}} \cdot \left(\sqrt[3]{\color{blue}{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}}} \cdot {\left(e^{\left|x\right|}\right)}^{\left(2 \cdot \left(-\left|x\right|\right)\right)}\right)}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]
  11. Using strategy rm

  12. Applied add-exp-logError: 10.6 bits

    \[\leadsto \frac{\color{blue}{e^{\log \left(1 \cdot 1 - \frac{1}{\frac{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}{1}} \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{\left|x\right|}\right)}^{\left(2 \cdot \left(-\left|x\right|\right)\right)}\right)\right)}}}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]

  13. SimplifiedError: 10.6 bits

    \[\leadsto \frac{e^{\color{blue}{\log \left(1 \cdot 1 - \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right) \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)}}}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]
  14. Using strategy rm

  15. Applied add-cube-cbrtError: 10.6 bits

    \[\leadsto \frac{e^{\color{blue}{\left(\sqrt[3]{\log \left(1 \cdot 1 - \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right) \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)} \cdot \sqrt[3]{\log \left(1 \cdot 1 - \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right) \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)}\right) \cdot \sqrt[3]{\log \left(1 \cdot 1 - \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right) \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)}}}}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]

  16. Applied exp-prodError: 10.6 bits

    \[\leadsto \frac{\color{blue}{{\left(e^{\sqrt[3]{\log \left(1 \cdot 1 - \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right) \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)} \cdot \sqrt[3]{\log \left(1 \cdot 1 - \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right) \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(1 \cdot 1 - \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right) \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)}\right)}}}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]

  17. SimplifiedError: 10.6 bits

    \[\leadsto \frac{{\color{blue}{\left({\left(e^{\sqrt[3]{\log \left(1 \cdot \left(1 - \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(1 \cdot \left(1 - \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)\right)}\right)}\right)}}^{\left(\sqrt[3]{\log \left(1 \cdot 1 - \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right) \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)}\right)}}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]

  18. Final simplificationError: 10.6 bits

    \[\leadsto \frac{{\left({\left(e^{\sqrt[3]{\log \left(1 \cdot \left(1 - \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)\right)}}\right)}^{\left(\sqrt[3]{\log \left(1 \cdot \left(1 - \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}} \cdot \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right)\right)\right)}\right)}\right)}^{\left(\sqrt[3]{\log \left(1 \cdot 1 - \left(\sqrt[3]{{\left(0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)\right)}^{6}} \cdot {\left(e^{-2}\right)}^{\left({\left(\left|x\right|\right)}^{2}\right)}\right) \cdot \left(1 \cdot \frac{1}{{\left(1 + 0.3275911 \cdot \left|x\right|\right)}^{2}}\right)\right)}\right)}}{1 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \frac{0.254829592 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-0.284496736 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(1.421413741 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot \left(-1.453152027 + \frac{1}{1 + 0.3275911 \cdot \left|x\right|} \cdot 1.061405429\right)\right)\right)}{e^{{\left(\left|x\right|\right)}^{2}}}}\]

Reproduce

herbie shell --seed 2020200 
(FPCore (x)
  :name "Jmat.Real.erf"
  :precision binary64
  (- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x)))))))